Object's coordinates are not influenced by constraint's influence?
Object drived by another is always represent by it's relative coordinates. If you parent a cube to an empty and you will move with empty, cube will have also zero in coordinates.

And I don't think there is a problem to animate Camera on top of the Constraint. But if you animated influence to zero on frame 149 and one to frame 150 somthere is not to much room for transition. Sorry if I understood you wrong.